I ran into a similar issue. For how managed resolve the Outlook 2013 synchronization issue see the discussion thread at:
iTunes compatibility with Outlook 2013
OK, I believe I have resolved the iTunes and Outlook 2013 issue (for me at least) -- here is what happened:
When I installed Office 2013 I had a Google and Hotmail account setup, in addition to my local PST folder. I had no email account associated with my "local" PST file. I used the local PST file to store my Contacts, Calendar, and Notes items. In my email configuration settings I had specified the Google email account as my primary/default account. When I uninstalled Office 2010 and then installed Office 2013, my Google OST file was set as the default data file (instead of the local PST file). Once I changed my default data file to the local PST file and restarted iTunes my Contacts, Calendar, and Notes items synced successfully.
To set your default DATA FILE in Outlook 2013:
File > Account Settings > Account Settings... > Data Files tab > select (highlight) the desired data file, click on the 'Set as Default' menu button.
I hope this helps other people.
Thank you -- Cameron